Tennis giant Serena Williams led the tributes, saying she was "literally in tears" watching his comeback performance.
Molinari was also magnanimous in his praise for Woods, who took full advantage of his playing-partners mistakes and reeled off three birdies in four holes from the 13th before closing out a momentous win amid jubilant scenes on and around the 18th green.
National Basketball Association stars LeBron James and Steph Curry also expressed their admiration, although Curry hoped for a little more from Woods as a result of him claiming a fifth green jacket.
However, dressed in his traditional final-round red shirt, Woods emerged from a back-nine showdown with two-time major victor Molinari to win his fifth Masters title and 15th major of a storied career that moves him three behind Jack Nicklaus' record haul of 18.
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After a day of deafening roars, Woods was overcome with emotion given his daughter, Sam, and son, Charlie, were standing beside the 18th green. I know that I made a few mistakes the last couple tournaments, but it just felt like it was there.
It's the first time Woods has won a major when he didn't hold the 54-hole lead, and sets a new record for the longest gap between Masters victories. "My dad was here in 1997 and now I'm the dad with two kids there".
The 43-year-old Woods started Sunday's final round joint second with fellow American Tony Finau, while Molinari was the man to catch, starting the day at 13-under 203.
Yes, he's a major champion again.
At Carnoustie it was Woods who stumbled on the back nine while leading. 79-year-old Nicklaus posted on Twitter. "I'm so happy for him and for the game of golf this is so fantastic".